A8739. Well-known Numbers

Numbers $k$ -bonacci ( $k$ is integer, $k>1$ ) are a generalization of Fibonacci numbers and are determined as follows:

- $F(k,n)=0$ , for integer $n$ , $1<=n<k$ ;
- $F(k,k)=1$ ;
- $F(k,n)=F(k,n-1)+F(k,n-2)+...+F(k,n-k)$ , for integer $n$ , $n>k$ .

Note that we determine the $k$ -bonacci numbers, $F(k,n)$ , only for integer values of $n$ and $k$ .

You've got a number $s$ , represent it as a sum of several (at least two) distinct $k$ -bonacci numbers.

The first line contains two integers $s$ and $k$ $(1<=s,k<=10^{9}; k>1)$ .

In the first line print an integer $m$ $(m>=2)$ that shows how many numbers are in the found representation. In the second line print $m$ distinct integers $a_{1},a_{2},...,a_{m}$ . Each printed integer should be a $k$ -bonacci number. The sum of printed integers must equal $s$ .

It is guaranteed that the answer exists. If there are several possible answers, print any of them.